According to the BBC news, since their introduction, both of these animals have had a dramatic impact on local ecology and are especially harmful to native species in the UK.
Scientists are unsure what will happen when the two alien invaders eventually cross paths.
Various sites around the UK have been highlighted as potential meeting places; they include the River Lee, in the South, and the River Ouse and the Aire in Yorkshire, writes Rebecca Morelle for the BBC.
The non-native crayfish was first introduced to the UK in the late 1970s for aquaculture, but it soon began to spread.
Several different species now exist in the UK's waterways, but the signal crayfish (Pacifastacus leniusculus), which comes from North America, has so far caused the most damage - thanks, in part, to a disease it carries. Where the non-natives move in, the white claws are lost.
Destructive Aquatic Aliens Meet on UK Shores
UK - Scientists believe that the ranges of the plague-carrying non-native crayfish and the fierce Chinese mitten crab are beginning to overlap.